Abstract

A sensitive differential method is described for isolating from other losses the residual reflectivity of an antireflection coating deposited on a quarterwave plate. Insertion of such a plate into a passive cavity reveals two eigenstates related to its axis, which may be by nature simultaneously resonant and antiresonant. The ratio between the two corresponding output intensities depends on the residual reflectivity of the plate and is moreover enhanced by the resonator. A residual reflectivity resolution of 10 ppm with a relatively low cavity finesse of 70 is achieved, and the possibility of measuring separately the losses from the coating and the substrate, using a half-coated quarterwave plate, is developed. We discuss the performances of our experimental setup and possible improvements and extensions of the method, in particular to isotropic components.

© 1988 Optical Society of America

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References

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  1. “Optical Coatings: the State of the Art,” Opt. News 12(8), (1986).
  2. H. P. Brändli, “Method for Measuring Small Optical Losses Using a He–Ne Laser,” Rev. Sci. Instrum. 39, 583 (1968).
    [CrossRef]
  3. V. Sanders, “High-Precision Reflectivity Measurement Technique for Low-Loss Laser Mirrors,” Appl. Opt. 16, 19 (1977).
    [CrossRef] [PubMed]
  4. J. M. Herbelin, J. A. McKay, M. A. Kwok, R. H. Ueunten, D. S. Urevig, D. J. Spencer, D. J. Benard, “Sensitive Measurement of Photon Lifetime and True Reflectances in an Optical Cavity by a Phase-Shift Method,” Appl. Opt. 19, 144 (1980).
    [CrossRef] [PubMed]
  5. D. Z. Anderson, J. C. Frisch, C. S. Masser, “Mirror Reflectometer Based on Optical Cavity Decay Time,” Appl. Opt. 23, 1238 (1984).
    [CrossRef] [PubMed]
  6. “Ultralow Loss Measurements for High Performance Optics,” Laser Focus/Electro-Opt.22 (Feb.1987).
  7. L. Cook, W. H. Lowdermilk, D. Milan, J. E. Swain, “Antireflective Surfaces for High-Energy Laser Optics Formed by Neutral-Solution Processing,” Appl. Opt. 21, 1482 (1982).
    [CrossRef] [PubMed]
  8. A. Le Floch, Thesis, Rennes (1977), unpublished; A. Le Floch, R. Le Naour, “Polarization Effects in Zeeman Lasers with x-y-Type Loss Anisotropies,” Phys. Rev. A 4, 290 (1971); A. Le Floch, R. Le Naour, G. Stephan, “Analysis of the Lamb-Dip Structure with Linear and Helicoīdal Polarizations,” Phys. Rev. Lett. 39, 1611 (1977).
    [CrossRef]
  9. A. Le Floch, P. Frère, P. Brun, “Frequency Stabilization of a Gas Laser Using the Magnetic Lamb-Dip,” Appl. Phys. Lett. 17, 40 (1970).
    [CrossRef]
  10. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986), p. 764.
  11. J. C. Kemp, “Piezo-optical Birefringence Modulators: New Use for a Long-Known Effect,” J. Opt. Soc. Am. 59, 950 (1969).
  12. J. Badoz, M. Billardon, J. C. Canit, M. F. Russel, “Sensitive Devices to Determine the State and Degree of Polarization of a Light Beam Using a Birefringence Modulator,” J. Opt. Paris 8, 373 (1977).
    [CrossRef]

1987 (1)

“Ultralow Loss Measurements for High Performance Optics,” Laser Focus/Electro-Opt.22 (Feb.1987).

1986 (1)

“Optical Coatings: the State of the Art,” Opt. News 12(8), (1986).

1984 (1)

1982 (1)

1980 (1)

1977 (2)

V. Sanders, “High-Precision Reflectivity Measurement Technique for Low-Loss Laser Mirrors,” Appl. Opt. 16, 19 (1977).
[CrossRef] [PubMed]

J. Badoz, M. Billardon, J. C. Canit, M. F. Russel, “Sensitive Devices to Determine the State and Degree of Polarization of a Light Beam Using a Birefringence Modulator,” J. Opt. Paris 8, 373 (1977).
[CrossRef]

1970 (1)

A. Le Floch, P. Frère, P. Brun, “Frequency Stabilization of a Gas Laser Using the Magnetic Lamb-Dip,” Appl. Phys. Lett. 17, 40 (1970).
[CrossRef]

1969 (1)

1968 (1)

H. P. Brändli, “Method for Measuring Small Optical Losses Using a He–Ne Laser,” Rev. Sci. Instrum. 39, 583 (1968).
[CrossRef]

Anderson, D. Z.

Badoz, J.

J. Badoz, M. Billardon, J. C. Canit, M. F. Russel, “Sensitive Devices to Determine the State and Degree of Polarization of a Light Beam Using a Birefringence Modulator,” J. Opt. Paris 8, 373 (1977).
[CrossRef]

Benard, D. J.

Billardon, M.

J. Badoz, M. Billardon, J. C. Canit, M. F. Russel, “Sensitive Devices to Determine the State and Degree of Polarization of a Light Beam Using a Birefringence Modulator,” J. Opt. Paris 8, 373 (1977).
[CrossRef]

Brändli, H. P.

H. P. Brändli, “Method for Measuring Small Optical Losses Using a He–Ne Laser,” Rev. Sci. Instrum. 39, 583 (1968).
[CrossRef]

Brun, P.

A. Le Floch, P. Frère, P. Brun, “Frequency Stabilization of a Gas Laser Using the Magnetic Lamb-Dip,” Appl. Phys. Lett. 17, 40 (1970).
[CrossRef]

Canit, J. C.

J. Badoz, M. Billardon, J. C. Canit, M. F. Russel, “Sensitive Devices to Determine the State and Degree of Polarization of a Light Beam Using a Birefringence Modulator,” J. Opt. Paris 8, 373 (1977).
[CrossRef]

Cook, L.

Frère, P.

A. Le Floch, P. Frère, P. Brun, “Frequency Stabilization of a Gas Laser Using the Magnetic Lamb-Dip,” Appl. Phys. Lett. 17, 40 (1970).
[CrossRef]

Frisch, J. C.

Herbelin, J. M.

Kemp, J. C.

Kwok, M. A.

Le Floch, A.

A. Le Floch, P. Frère, P. Brun, “Frequency Stabilization of a Gas Laser Using the Magnetic Lamb-Dip,” Appl. Phys. Lett. 17, 40 (1970).
[CrossRef]

A. Le Floch, Thesis, Rennes (1977), unpublished; A. Le Floch, R. Le Naour, “Polarization Effects in Zeeman Lasers with x-y-Type Loss Anisotropies,” Phys. Rev. A 4, 290 (1971); A. Le Floch, R. Le Naour, G. Stephan, “Analysis of the Lamb-Dip Structure with Linear and Helicoīdal Polarizations,” Phys. Rev. Lett. 39, 1611 (1977).
[CrossRef]

Lowdermilk, W. H.

Masser, C. S.

McKay, J. A.

Milan, D.

Russel, M. F.

J. Badoz, M. Billardon, J. C. Canit, M. F. Russel, “Sensitive Devices to Determine the State and Degree of Polarization of a Light Beam Using a Birefringence Modulator,” J. Opt. Paris 8, 373 (1977).
[CrossRef]

Sanders, V.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986), p. 764.

Spencer, D. J.

Swain, J. E.

Ueunten, R. H.

Urevig, D. S.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

A. Le Floch, P. Frère, P. Brun, “Frequency Stabilization of a Gas Laser Using the Magnetic Lamb-Dip,” Appl. Phys. Lett. 17, 40 (1970).
[CrossRef]

J. Opt. Paris (1)

J. Badoz, M. Billardon, J. C. Canit, M. F. Russel, “Sensitive Devices to Determine the State and Degree of Polarization of a Light Beam Using a Birefringence Modulator,” J. Opt. Paris 8, 373 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

Laser Focus/Electro-Opt. (1)

“Ultralow Loss Measurements for High Performance Optics,” Laser Focus/Electro-Opt.22 (Feb.1987).

Opt. News (1)

“Optical Coatings: the State of the Art,” Opt. News 12(8), (1986).

Rev. Sci. Instrum. (1)

H. P. Brändli, “Method for Measuring Small Optical Losses Using a He–Ne Laser,” Rev. Sci. Instrum. 39, 583 (1968).
[CrossRef]

Other (2)

A. Le Floch, Thesis, Rennes (1977), unpublished; A. Le Floch, R. Le Naour, “Polarization Effects in Zeeman Lasers with x-y-Type Loss Anisotropies,” Phys. Rev. A 4, 290 (1971); A. Le Floch, R. Le Naour, G. Stephan, “Analysis of the Lamb-Dip Structure with Linear and Helicoīdal Polarizations,” Phys. Rev. Lett. 39, 1611 (1977).
[CrossRef]

A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986), p. 764.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup and distribution of polarizations: OI, optical isolator; P1, input polarizer which fixes the input polarization E0; M1, M2, cavity mirrors; λ/4, quarterwave plate; COA, crystalline optic axis; E+45°, E−45°, the two eigenstates of the cavity; PZT, piezoelectric transducer; P2, output polarizer.

Fig. 2
Fig. 2

Three oscilloscope traces showing the output intensities with the same scale vs the phase shift ϕ of the cavity for three orientations of P2: trace 1, P2 parallel to E0; trace 2, P2 at +45° from E0; trace 3, P2 at −45° from E0.

Fig. 3
Fig. 3

Evolution of the two output peaks vs the optical thickness of the quarterwave plate in wavelength units. The first four peaks concern the state 1 at +45° from E0, the four others the state 2 at −45° from E0.

Fig. 4
Fig. 4

(a) Output intensity vs the phase shift ϕ of the cavity without P2; (b) theoretical fit of (a) for R p = 0.23% and F r = 70.

Fig. 5
Fig. 5

Relative dispersion of the mean values of the ratio K r /K a vs the number N of averaged acquisitions.

Fig. 6
Fig. 6

(a) Output intensity vs the phase shift ϕ of the high finesse cavity. The frequency scan of the cavity is 2 Hz. The weak peak between a and r is due to the excitation of the TEM01 mode which results from imperfect matching. (b) The theoretical fit of (a) for R p = 0.23% and F r = 600.

Fig. 7
Fig. 7

Output intensity vs the phase shift ϕ of the high finesse cavity containing the half-coated quarterwave plate in (a) the coated area, (b) the uncoated area. The scale for intensities is the same for the two photos.

Equations (14)

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T r = T p 2 ( 1 - A s ) [ 1 - R p ( 1 - A s ) ] 2 ,
T a = T p 2 ( 1 - A s ) [ 1 + R p ( 1 - A s ) ] 2 .
T p + R p + A p = 1 ,
T r 1 - 2 A p - A s ,
T a T r - 4 R p .
K r / K a = T r / T a · ( 1 - R · T a 1 - R · T r ) 2 ,
K r / K a ( 1 + 4 R · R p 1 - R · T r ) 2 .
F r = π · ( R · T r ) 1 / 2 ( 1 - R · T r ) .
K r / K a ( 1 + 4 π · F r · R p ) 2 .
R p π 4 · F r [ ( K r / K a ) 1 / 2 - 1 ] .
K r / K a = ( K r 1 · K r 2 K a 2 · K a 1 ) 1 / 2
T r u 1 - A s ,
A p π 2 · F r u [ ( K r u / K r ) 1 / 2 - 1 ] ,
A s π F [ ( K / 2 K r u ) 1 / 2 - 1 ] ,

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